Multiple-Access Channel with Independent Sources: Error Exponent Analysis

TL;DR

This paper derives an achievable error exponent for a multiple-access channel with two independent sources, optimizing codebook partitioning and providing bounds that improve understanding of error performance.

Contribution

It introduces a new method for partitioning source messages and derives bounds for the error exponent, enhancing coding strategies for multiple-access channels.

Findings

Optimized partitioning thresholds maximize the error exponent.

Derived bounds relate to Gallager's source and channel functions.

Numerical example shows improved error exponents over i.i.d. codebooks.

Abstract

In this paper, an achievable error exponent for the multiple-access channel with two independent sources is derived. For each user, the source messages are partitioned into two classes and codebooks are generated by drawing codewords from an input distribution depending on the class index of the source message. The partitioning thresholds that maximize the achievable exponent are given by the solution of a system of equations. We also derive both lower and upper bounds for the achievable exponent in terms of Gallager's source and channel functions. Finally, a numerical example shows that using the proposed ensemble gives a noticeable gain in terms of exponent with respect to independent identically distributed codebooks.